Algebraic connectivity of $k$-connected graphs

Kirkland, Stephen J., Rocha, Israel, and Trevisan, Vilmar. "Algebraic connectivity of $k$-connected graphs." Czechoslovak Mathematical Journal 65.1 (2015): 219-236. <http://eudml.org/doc/270032>.

@article{Kirkland2015,
abstract = {Let $G$ be a $k$-connected graph with $k \ge 2$. A hinge is a subset of $k$ vertices whose deletion from $G$ yields a disconnected graph. We consider the algebraic connectivity and Fiedler vectors of such graphs, paying special attention to the signs of the entries in Fiedler vectors corresponding to vertices in a hinge, and to vertices in the connected components at a hinge. The results extend those in Fiedler’s papers Algebraic connectivity of graphs (1973), A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory (1975), and Kirkland and Fallat’s paper Perron Components and Algebraic Connectivity for Weighted Graphs (1998).},
author = {Kirkland, Stephen J., Rocha, Israel, Trevisan, Vilmar},
journal = {Czechoslovak Mathematical Journal},
keywords = {algebraic connectivity; Fiedler vector},
language = {eng},
number = {1},
pages = {219-236},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Algebraic connectivity of $k$-connected graphs},
url = {http://eudml.org/doc/270032},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Kirkland, Stephen J.
AU - Rocha, Israel
AU - Trevisan, Vilmar
TI - Algebraic connectivity of $k$-connected graphs
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 1
SP - 219
EP - 236
AB - Let $G$ be a $k$-connected graph with $k \ge 2$. A hinge is a subset of $k$ vertices whose deletion from $G$ yields a disconnected graph. We consider the algebraic connectivity and Fiedler vectors of such graphs, paying special attention to the signs of the entries in Fiedler vectors corresponding to vertices in a hinge, and to vertices in the connected components at a hinge. The results extend those in Fiedler’s papers Algebraic connectivity of graphs (1973), A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory (1975), and Kirkland and Fallat’s paper Perron Components and Algebraic Connectivity for Weighted Graphs (1998).
LA - eng
KW - algebraic connectivity; Fiedler vector
UR - http://eudml.org/doc/270032
ER -